In the era of artificial intelligence, there has been a growing consensus that solutions to complex science and engineering problems require novel methodologies that can integrate interpretable physics-based modeling approaches with machine learning techniques, from stochastic optimization to deep neural networks. This thesis aims to develop new methodological and applied frameworks for combining the advantages of physics-based modeling and machine learning, with special attention to two important signal processing tasks: solving inverse problems in hyperspectral imaging and detecting changepoints in time series. The first part of the thesis addresses learning priors in model-based optimization for solving inverse problems in hyperspectral imaging systems. First, we introduce a tuning-free Plug-and-Play algorithm for hyperspectral image deconvolution (HID). Specifically, we decompose the optimization problem into two iterative sub-problems, learn deep priors to solve the blind denoising sub-problem with neural networks, and estimate hyperparameters with ...

The necessity to process signals living in non-Euclidean domains, such as signals de- fined on the top of a graph, has led to the extension of signal processing techniques to the graph setting. Among different approaches, graph signal processing distinguishes it- self by providing a Fourier analysis of these signals. Analogously to the Fourier transform for time and image signals, the graph Fourier transform decomposes the graph signals in terms of the harmonics provided by the underlying topology. For instance, a graph signal characterized by a slow variation between adjacent nodes has a low frequency content. Along with the graph Fourier transform, graph filters are the key tool to alter the graph frequency content of a graph signal. This thesis focuses on graph filters that are performed distributively in the node domain–that is, each node needs to exchange in- formation ...

To the surprise of most of us, complexity in nature spawns from simplicity. No matter how simple a basic unit is, when many of them work together, the interactions among these units lead to complexity. This complexity is present in the spreading of diseases, where slightly different policies, or conditions,might lead to very different results; or in biological systems where the interactions between elements maintain the delicate balance that keep life running. Fortunately, despite their complexity, current advances in technology have allowed us to have more than just a sneak-peak at these systems. With new views on how to observe such systems and gather data, we aimto understand the complexity within. One of these new views comes from the field of graph signal processing which provides models and tools to understand and process data coming from such complex systems. With ...

The abundance of large and heterogeneous systems is rendering contemporary data more pervasive, intricate, and with a non-regular structure. With classical techniques facing troubles to deal with the irregular (non-Euclidean) domain where the signals are defined, a popular approach at the heart of graph signal processing (GSP) is to: (i) represent the underlying support via a graph and (ii) exploit the topology of this graph to process the signals at hand. In addition to the irregular structure of the signals, another critical limitation is that the observed data is prone to the presence of perturbations, which, in the context of GSP, may affect not only the observed signals but also the topology of the supporting graph. Ignoring the presence of perturbations, along with the couplings between the errors in the signal and the errors in their support, can drastically hinder ...

Sound Source Localization (SSL) is the topic within acoustic signal processing which studies methods for the estimation of the position of one or more active sound sources in space, such as human talkers, using signals captured by one or more microphone arrays. It has many applications, including robot orientation, speech enhancement and diarization. Although signal processing-based algorithms have been the standard choice for SSL over past decades, deep neural networks have recently achieved state-of-the-art performance for this task. A drawback of most deep learning-based SSL methods consists of requiring the training and testing microphone and room geometry to be matched, restricting practical applications of available models. This is particularly relevant when using Distributed Microphone Arrays (DMAs), whose positions are usually set arbitrarily and may change with time. Flexibility to microphone geometry is also desirable for companies maintaining multiple types of ...

The scoring of a subject's sleep stages from electroencephalographic (EEG) signals is a costly process. As such, many approaches to its automation have been proposed, including ones based on Deep Learning. However, said approaches have yet to attain a level of performance good enough for use in clinical settings, in part due to the high variability between EEG recordings, and the challenges inherent to the classification of signals recorded in different environments.In this thesis, we tackle this issue through a novel angle, by representing each epoch within our EEG signals as a timeseries of covariance matrices. Said matrices, although a common tool for EEG analysis in Brain-Computer Interfaces (BCI), are not typically utilized in sleep stage scoring.Covariance matrices tend to be symmetric positive definite (SPD), with the set of SPD matrices forming a non-Euclidean Riemannian manifold. As such, a Euclidean ...

Acquisition is the first stage of a Global Navigation Satellite System (GNSS) receiver and has the goal to determine which signals are in view and provide rough estimates of the signal parameters. The main objective of the thesis was to provide a complete and cohesive analysis of the acquisition process clarifying different aspects often neglected in the literature. The thesis provides the statistical tools required for the characterization of the acquisition process. In particular, the signal presence is determined by searching several candidates for the signal code delay and Doppler frequency which define a cell of the acquisition search space. Thus, the acquisition process is characterized by the strategy adopted for searching for the signal parameters and the way a decision metric is compute for each cell of the search space. Given this observation, the thesis introduces the concepts of ...

Extending the concepts of classical signal processing to graphs, a wide array of methods have come to the fore, including filtering, reconstruction, classification, and sampling. Existing approaches in graph signal processing consider a known and static topology, i.e., fixed number of nodes and a fixed edge support. Two types of tasks stand out, namely, topology inference, where the edge support along with their weights are estimated from signals; and data processing, where existing data and the known topology are used to perform different tasks. However, such tasks become quite challenging when the network size and support changes over time. Particularly, these challenges involve adapting to the changing topology, data distributions and dealing with unknown topological information. The latter manifests for example, when new nodes are available to attach to the graph but their connectivity is uncertain as is the case ...

Modeling dynamical systems is a fundamental task in various scientific and engineering domains, requiring accurate predictions, robustness to varying conditions, and interpretability of the underlying mechanisms. Traditional data-driven approaches often struggle with long-term prediction accuracy, generalization to out-of-distribution (OOD) scenarios, and providing insights into the system's behavior. This thesis explores the integration of supervised disentanglement into deep learning models as a means to address these challenges. We begin by advancing the state-of-the-art in modeling wave propagation governed by the Saint-Venant equations. Utilizing U-Net architectures and purposefully designed training strategies, we develop deep learning models that significantly improve prediction accuracy. Through OOD analysis, we highlight the limitations of standard deep learning models in capturing complex spatiotemporal dynamics, demonstrating how integrating domain knowledge through architectural design and training practices can enhance model performance. We further extend our supervised disentanglement approach to high-dimensional ...

Machine learning and deep learning techniques have emerged as powerful tools for addressing complex challenges across diverse domains. These methodologies are powerful because they extract patterns and insights from large and complex datasets, automate decision-making processes, and continuously improve over time. They enable us to observe and quantify patterns in data that a normal human would not be able to capture, leading to deeper insights and more accurate predictions. This dissertation presents two research papers that leverage these methodologies to tackle distinct yet interconnected problems in neuroimaging and computer vision for the quantification of human health. The first investigation, "Age prediction using resting-state functional MRI," addresses the challenge of understanding brain aging. By employing the Least Absolute Shrinkage and Selection Operator (LASSO) on resting-state functional MRI (rsfMRI) data, we identify the most predictive correlations related to brain age. Our study, ...

High dimensional time series data are observed in many complex systems. In networked data, some of the time series are influenced by other time series. Identifying these relations encoded in a graph structure or topology among the time series is of paramount interest in certain applications since the identifi ed structure can provide insights about the underlying system and can assist in inference tasks. In practice, the underlying topology is usually sparse, that is, not all the participating time series influence each other. The goal of this dissertation pertains to study the problem of sparse topology identi fication under various settings. Topology identi fication from time series is a challenging task. The first major challenge in topology identi fication is that the assumption of static topology does not hold always in practice since most of the practical systems are evolving ...

The cumulative impact of co-channel interferers, commonly referred to as aggregate network interference, is one of the main performance limiting factors in today’s mobile cellular networks. Thus, its careful statistical description is decisive for system analysis and design. A system model for interference analysis is required to capture essential network variation effects, such as base station deployment- and signal propagation characteristics. Furthermore it should be simple and tractable so as to enable first-order insights on design fundamentals and rapid exchange of new ideas. Interference modeling has posed a challenge ever since the establishment of traditional macro cellular deployments. The recent emergence of heterogeneous network topologies complicates matters by contesting many established aspects of time-honored approaches. This thesis presents user-centric system models that enable to investigate scenarios with an asymmetric interference impact. The first approach simplifies the interference analysis in a ...

Cellular Neural Networks are characterized by simplicity of operation. The network consists of a large number of nonlinear processing units; called cells; that are equally spread in the space. Each cell has a simple function (sequence of multiply-add followed by a single discrimination) that takes an element of a topographic map and then interacts with all cells within a specified sphere of interest through direct connections. Due to their intrinsic parallel computing power, CNNs have attracted the attention of a wide variety of scientists in, e.g., the fields of image and video processing, robotics and higher brain functions. Simplicity of operation together with the local connectivity gives CNNs first-hand advantages for tiled VLSI implementations with very high speed and complexity. The first VLSI implementation has been based on analogue technology but was small and suffered from parasitic capacitances and resistances ...

Video signals are sequences of natural images, where images are often modeled as piecewise-smooth signals. Hence, video can be seen as a 3D piecewise-smooth signal made of piecewise-smooth regions that move through time. Based on the piecewise-smooth model and on related theoretical work on rate-distortion performance of wavelet and oracle based coding schemes, one can better analyze the appropriate coding strategies that adaptive video codecs need to implement in order to be efficient. Efficient video representations for coding purposes require the use of adaptive signal decompositions able to capture appropriately the structure and redundancy appearing in video signals. Adaptivity needs to be such that it allows for proper modeling of signals in order to represent these with the lowest possible coding cost. Video is a very structured signal with high geometric content. This includes temporal geometry (normally represented by motion ...

In the world of Information and communications technology (ICT), strategies for innovation and development are increasingly focusing on applications that require spatial representation and real-time interaction with and within 3D-media environments. One of the major challenges that such applications have to address is user-centricity, reflecting e.g. on developing complexity-hiding services so that people can personalize their own delivery of services. In these terms, multimodal interfaces represent a key factor for enabling an inclusive use of new technologies by everyone. In order to achieve this, multimodal realistic models that describe our environment are needed, and in particular models that accurately describe the acoustics of the environment and communication through the auditory modality are required. Examples of currently active research directions and application areas include 3DTV and future internet, 3D visual-sound scene coding, transmission and reconstruction and teleconferencing systems, to name but ...